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The students will need to have a clear understanding of the relationship between the ratio table and the coordinate grid. This was addressed in a prior lesson which is located in their 6th grade tool box. Many times students view graphing as completely unrelated to ratios. It will be very important for us to make that connection for them and to get them to realize that graphing provides another way of looking at this relationship. Additionally, it may be a good idea to review order pairs and how they are plotted on the grid as this becomes a problem for students who have limited knowledge of this concept.

Start by asking students to find at least 3 equivalent ratios to 4/16 by using a ratio table. Randomly ask students for their ratios and place them in the chart. Then, show them the coordinate grid and explain/remind them that the first number (numerator) belongs on the x axis and the second number (denominator) belongs on the y axis. Model out loud how to graph the points the students gave you. Ask the students what they notice about the relationship between the table and the graph(SMP 7: structure). Next, ask the students to find two additional points from the line. Have students justify that these two points are still equivalent ratios? (SMP 3: arguing). As an extension to this questioning, ask the students if they can make a generalization about all the points on the line?(SMP 8: Patterns) I’m looking for students to say that all points on the line are equivalent ratios if they form a straight line. Also, students might say that they can easily check their work by plotting it on the grid because it will form a straight line.

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In this section, I’m going to bring back the tables from the Equivalent ratio and tables worksheet from the DO NOW acitivity. I’m going to have students use these tables and plot the points on the coordinate grid. Students will quickly see that there work is correct as the plotted points form a line. As an extension, I’m going to have the students use the graph to find a value that is not in the table. Then I will have them put it in the table to justify their answer is correct. (SMP 6)

I’m going to use the In-Class worksheet (Massachusetts DOE, 2012), to let them practice on their own. While the students are practicing, I’m going to walk around to check for understanding. At this time, students should be working independently, but can use their tablemates for assistance.

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To bring this lesson to a close, I’m going to have the students create their own ratio table and graph it on the grid. I will then ask them if there graph shows a ratio and how they know? Then, I will ask them to use the grid and find a ratio that is not from their table and to justify their answer.

Big Idea:
Ben’s mom gives him the option of grooming 3 horses or mowing 2 fields. Which job should Ben choose? Why? Students use their knowledge of algebraic expressions and equations to write expressions and equations.